Magnetic gradiometer and magnetic sensing method

ABSTRACT

A gradiometer in which a probe beam for reading sequentially passes through two magnetic field measurement regions to obtain signals according to magnetic flux densities of the respective regions is formed using an optically pumped magnetometer. In particular, in a gradiometer using a high sensitivity optically pumped magnetometer, a geometric arrangement enabling obtainment of a large signal from a dipole moment as a signal source is defined.

TECHNICAL FIELD

The present invention relates to a magnetometer that measures a strengthof a magnetic field. Specifically, the present invention relates to agradiometer and a magnetic sensing method, which use an optically pumpedmagnetometer.

BACKGROUND ART

In many cases, for measuring a weak magnetic field, a magneticgradiometer (hereinafter also simply referred to as “gradiometer”) isformed using measurement data obtained by magnetometers for two or moremagnetic field measurement regions. As an example of such gradiometer, agradiometer using an optically pumped magnetometer is known. Anoptically pumped magnetometer applies a pump beam to a magnetic fieldmeasurement region with a group of gaseous atoms encapsulated therein tocause spin polarization and obtain a rotation of a polarization planeoccurring when a probe beam for reading is made to pass through theregion, as a signal according to a magnetic flux density of the region.Use of optically pumped magnetometers to obtain a difference betweensignals obtained in two respective magnetic field measurement regionswhen a probe beam has sequentially passed through the magnetic fieldmeasurement regions enables formation of a gradiometer. As an example ofa high-sensitivity optically pumped magnetometer that can be used toform a gradiometer, U.S. Pat. No. 7,038,450 proposes an atomic magneticsensor using a circularly-polarized beam as a pump beam and alinearly-polarized beam of light as a probe beam, for a cell in whichalkali metal vapor is present.

However, for such gradiometer using optically pumped magnetometers,there have been no discussions ever before on an optimum geometricarrangement of a signal source and two magnetic field measurementregions and an optimum direction of a magnetic field to which themagnetometers respond in the two magnetic field measurement regions.

CITATION LIST Patent Literature

PTL 1: U.S. Pat. No. 7,038,450

SUMMARY OF INVENTION

The present invention is directed to a gradiometer enabling highersensitivity measurement of a magnetic field and S/N ratio improvement,which has been obtained as a result of studies on effects of angeometric arrangement of a signal source and two magnetic fieldmeasurement regions and a direction of a magnetic field to which themagnetometer respond in the two magnetic field measurement regionsimposed on a gradiometer.

In a gradiometer using an optically pumped magnetometer according to thepresent invention, the gradiometer using the optically pumpedmagnetometer includes: a cell containing a group of atoms in a gaseousstate, including an alkali metal, encapsulated therein; a pump beamsource that applies a first pump beam and a second pump beam to the cellto spin-polarize the group of atoms, the first pump beam and the secondpump beam being parallel to each other; a probe beam source that appliesa probe beam to the cell; a detector for detecting a rotation of apolarization plane of the probe beam that has passed through the cell ina state in which the group of atoms is spin-polarized, wherein the firstpump beam and the probe beam cross each other at a first measurementposition, the second pump beam and the probe beam crosses each other ata second measurement position, the first measurement position and thesecond measurement position are arranged along a first direction that islinear with respect to a signal source, and the probe beam sequentiallypasses through the first measurement region and the second measurementregion; wherein an alkali metal density, a measurement position length,a pump beam intensity and a spin polarization ratio for the firstmeasurement position are the same as those of the second measurementposition; and wherein each of a direction of a magnetic field measuredat the first measurement position and a direction of a magnetic fieldmeasured at the second measurement position is the same as the firstdirection, a sign of spin polarization caused by optical pumping isdifferent between the first measurement region and the secondmeasurement region; and an angle of rotation of the polarization planeof the probe beam that has sequentially passed through each of the firstmeasurement position and the second measurement position is obtained,thereby obtaining a difference in magnetic flux density between thefirst measurement position and the second measurement position.

According to the present invention, a gradiometer enabling highsensitivity measurement of a magnetic field from a magnetic moment,which is a signal source, and S/N ratio improvement can be formed.

Further features of the present invention will become apparent from thefollowing description of exemplary embodiments with reference to theattached drawings.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic diagram illustrating a gradiometer according to afirst example of the present invention.

FIGS. 2A and 2B are schematic diagrams illustrating a mirror used in avariation of the first example of the present invention.

FIGS. 3A and 3B are schematic diagrams illustrating a total reflectionprism used in a variation of the first example of the present invention.

FIG. 4 is a schematic diagram illustrating a gradiometer according to asecond example of the present invention.

FIG. 5 is a schematic diagram illustrating a gradiometer according to avariation of the second example of the present invention.

FIG. 6 is a schematic diagram illustrating a gradiometer according to athird example of the present invention.

DESCRIPTION OF EMBODIMENTS

An exemplary mode for carrying out the present invention will bedescribed below based on an embodiment.

Gradiometer

First, a relationship between a configuration of a gradiometer andstrengths of a signal and noise obtained by such configuration will bediscussed. Considering a magnetic field produced by a magnetic momentm_(S), a magnetic flux density vector B(d) at a position away from themagnetic moment m_(S), which is an attentioned magnetic signal source,by a distance vector d can be expressed by

$\begin{matrix}{{B(d)} = {\frac{\mu_{0}}{4\pi}\left\lbrack \frac{{3{n\left( {n \cdot m_{S}} \right)}} - m_{S}}{{d}^{3}} \right\rbrack}} & (1)\end{matrix}$

wherein μ₀ is a vacuum magnetic permeability, a vector n is a unitvector pointing to a direction of the vector d. Based on expression (1),where the direction of the magnetic moment m_(S) points to a directionfrom the signal source toward the magnetometer (direction of the vectorn), a magnitude of the magnetic flux density vector at the position ofthe magnetometer can be expressed by

|B(d)|=μ₀ ×|m _(S)|/(2×d ³×π)  (2).

This is also a maximum value of the magnetic flux density that can bedetected by the magnetometer under the condition that the absolute valueof d, i.e., |d|, is constant.

Then, another magnetometer is arranged to form a gradiometer of a simplemodel in which the two magnetometers are arranged on a straight line andthe direction of the magnetic moment m_(S) points to a direction fromthe signal source toward the two magnetometers. Where distances to twomagnetometers are d₁ and d₂ (d₁<d₂), if a signal measured at theposition of the distance d₂ is subtracted from a signal measured at theposition of the distance d₁, a resulting signal S can be expressed by

S=μ ₀ ×|m _(S)|/(2×π)×(d ₁ ⁻³ −d ₂ ⁻³)=μ₀ ×|m _(S)|/(2×d ₁ ³×π)×[1−(d ₁/d ₂)³]  (3).

For example, where d₂=2×d₁, it can be understood from expression (3)that the decrease of the signal remains at approximately ⅛. In otherwords, with this model, a strength of a magnetic signal from thevicinity of the sensor is substantially maintained.

Meanwhile, magnetic field noise from a position that is very fartherthan the attentioned signal source can also be considered as a magneticfield created by another magnetic moment m_(N). Where distances from themagnetic moment m_(N), which is a noise source, to the two magnetometersare R₁ and R₂, a noise component N from the noise source can be obtainedby a signal measured at the position of the distance R₂ is subtractedfrom a signal measured at the position of the distance R₁, and can beexpressed by

N=μ ₀ ×|m _(N)|/(2×R ₁ ³×π)×[1−(R ₁ /R ₂)³]  (4.

Since R₁≈R₂ in the case of a distant noise source, it can be understoodthat in this model, noise described by a distantly-arranged magneticmoment can substantially be reduced.

As described above, a configuration in which two magnetic fieldmeasurement regions are arranged to be linear with respect to a signalsource and a direction of a magnetic moment m_(S) points to a directionfrom the signal source toward the two magnetic field measurement regionsenables reduction of noise from a distance position while maintainingthe strength of a magnetic signal from the vicinity of the sensor.

Optically Pumped Magnetometer

Next, an optically pumped magnetometer used in a gradiometer accordingto the present invention for magnetic signal detection will bediscussed.

A. Principle of Operation of an Optically Pumped Magnetometer

First, operation of an optically pumped magnetometer will be describedaccording to three steps below.

1) A pump beam is applied to an alkali metal gas encapsulated in a cellto orient spin of electrons in the atoms, thereby producing spinpolarization. For the pump beam, a beam with a wavelength causing anoptical transition from a ground level to an excited level, such as D1transition of an alkali metal, is used. Where a circularly-polarizedbeam is used for the pump beam, the circularly-polarized beam isabsorbed by the electrons in a particular spin state, providing anoptical pumping effect, enabling provision of spin polarization for thealkali metal.

The spin polarization can be provided by circularly-polarized beam usedas a pump beam because of conservation of angular momentum. A photon ofcircularly-polarized light has an angular momentum, and only a pair of aground level and an excited level that can receive the angular momentumfrom the photon can be excited. For example, right-handcircularly-polarized light is selectively absorbed by a pair of a groundlevel and an excited level that increases an angular momentum of eachelectron by a quantum number of 1. The once excited atoms return to theground state after emitting randomly-polarized light by means ofspontaneous emission, or through, e.g., collision with quencher gasatoms. In this state, atoms with their angular momentums decreased by aquantum number of 1 and atoms returning to the ground state with theirangular momentums conserved are mixed. Hence, repetition of a randomexcitation and relaxation process increases the ratio of atoms in whichthe ground state are not excited by the circularly-polarized light. As aresult, the direction of the spin of atoms included in the group ofatoms are oriented in the direction of travel of thecircularly-polarized light as an axis of the quantization. In order toenhance the density of the alkali metal gas in the cell, the cell may beheated to a maximum of around 200° C.

2) Spin polarization of the alkali metal rotates upon reception of atorque in a magnetic field. It is known that use of optical Blochequation (5) including effects of pumping and relaxation ofoptically-pumped spin enables description of the behavior of a spinpolarization vector P in a magnetic field

$\begin{matrix}{\frac{P}{t} = {{\frac{\gamma_{e}}{Q}B \times P} - {\Gamma_{eff}P} + R}} & (5)\end{matrix}$

wherein γ_(e) is a gyromagnetic ratio of an electron, Q is a slowdownfactor depending on a spin polarization ratio, Γ_(eff) is a spinrelaxation rate, B is a magnetic field vector and R is a pumping vector.

3) Information on the spin polarization in the magnetic field is read bymeans of a probe beam which is a linearly-polarized beam. Where spinpolarization has a component in the direction of propagation of theprobe beam, the magnitude of the spin polarization can be read as arotation of a polarization plane caused by a magnetooptic effect. Forthe probe beam, also, a beam with a wavelength around a resonantwavelength of the alkali metal is used. Thus, the wavelength is made tobe detuned from a center of the resonance, thereby reducing effects ofthe probe beam on the optical absorption and the spin polarization.

The probe beam, which is a linearly-polarized beam, can be described assuperimposition of both a left-hand circularly-polarized beam and aright-hand circularly-polarized beam. As also mentioned in thedescription of the pump beam, a circularly-polarized beam of light isabsorbed by electrons in a particular spin state, and thus, ifpolarization occurs in the atom group, a difference in absorption occursbetween the left-hand circularly-polarized beam and the right-handcircularly-polarized beam depending on the polarization. A difference inabsorption coefficient means an imaginary part of a complex refractiveindex, and thus, a difference occurs between the real parts of therefractive indexes sensed by the left-hand circularly-polarized beam andthe right-hand circularly-polarized beam according to the Kramers-Kronigrelation. Therefore, use of a linearly-polarized beam obtained bysuperimposition of both a left-hand circularly-polarized beam and aright-hand circularly-polarized beam causes a difference in lengthbetween the optical paths of the left-hand circularly-polarized beam andthe right-hand circularly-polarized beam when the linearly-polarizedbeam passing through the atom group, and thus, a rotation of thepolarization plane is observed.

Since the angle of such rotation depends on the magnitude of themagnetic field, measurement of the angle of rotation of the polarizationplane enables detection of the magnitude of the magnetic field.

Next, a relationship between a direction of a magnetic field measured bya magnetometer and a strength of an obtained signal will be describedfor two operating modes of an optically pumped magnetometer: azero-magnetic field magnetometer and a resonant operation of amagnetometer.

B. Zero-Magnetic Field Magnetometer

In a state of a zero-magnetic field magnetometer, a magnetic field of amagnetic field measurement region in which an alkali metal gas, to whicha pump beam and a probe beam are applied, is placed so as to adjust astrength to be no more than about 1 nT (nanotesla). The gyromagneticratio of an alkali metal is, e.g., 7 GHz/T for K, 4.6 GHz/T for ⁸⁵Rb, 7GHz/T for ⁸⁷Rb and 3.5 GHz/T for Cs. In any case, for a magnetic fieldof no more than 1 nT, an optically pumped magnetometer acts as azero-magnetic field magnetometer with a Larmor frequency of no more than10 Hz. In this condition, in solving optical Bloch equation (5), thebehavior of spin polarization can well be descried according to astationary solution that temporal change of the spin polarization iszero.

In the zero-magnetic field magnetometer, spin polarization in proportionto a magnetic field of a component orthogonal to the pump beam and theprobe beam is induced in the direction of the probe beam. In otherwords, the magnetometer has substantive sensitivity to a magnetic fieldin the direction orthogonal to both the pump beam and the probe beam.

When measuring a biometric magnetic field resulting from activities of abrain and/or a heart, a direction of a magnetic moment m_(S) is not aparameter that a measurement system can select. Nevertheless, in orderto confirm the fact that the strength of an obtained signal variesdepending on the direction of a magnetic field measured by themagnetometer, the magnitude of the magnetic flux density is figured outbased on expression (1) for two cases below.

(i) A case where the magnetic moment m_(S) points to the direction ofthe vector n

Since an n-direction component of a magnetic field is measured, a signalwhose magnetic flux density has a magnitude of

μ₀×2|m_(S)|/(4π×d₁ ³) is measured.

(ii) A case where the magnetic moment m_(S) points to a directionorthogonal to the vector n

Since a component parallel to the magnetic moment m_(S) is measured, asignal whose magnetic flux density has a magnitude of

−μ₀×|m_(S)|/(4π×d₁ ³) is measured.

As can be seen from the above discussion, a larger signal can beobserved in the case where the magnetic moment m_(S) points to thedirection of the vector n (case 1).

C. Resonant Operation of a Magnetometer

Also, a bias magnetic field of no less than 1 nT can be applied in thepump beam direction to make a magnetometer to perform a resonantoperation. In this case, spin polarization resulting from opticalpumping precesses at a Larmor frequency determined by the magnitude ofthe bias magnetic field with the direction of the bias magnetic field asa rotation axis. Motion of spin polarization with this magnetometer isdescribed by means of, in particular, a stationary solution oscillatingat a Larmor procession frequency from among the optical Bloch equationsolutions.

This stationary solution is coupled with a magnetic field oscillating ata Larmor procession frequency, resulting in change in the direction ofthe spin polarization. From analysis of the optical Bloch equations, itis known that where a magnetometer performs a resonant operation, themagnetometer performs the resonant operation at a Larmor processionfrequency for not only a magnetic field in the direction orthogonal toboth the pump beam and the probe beam, but also a magnetic field in theprobe direction.

A magnetic resonant signal is measured using such magnetometer. A statein which a magnetic moment m_(S), which is a signal source, rotates bymeans of magnetic resonance at an angular frequency ω will beconsidered. For measurement of a magnetic field as a magnetic resonantsignal at a position a distance d₁ away, the bias magnetic field in themagnetometer is adjusted to make the resonant frequency correspond to arotation frequency of the magnetic moment within a resonance width. Inthis case, the magnitude of the detected signal varies depending on thecombination of the direction of the axis of rotation of the magneticmoment m_(S) and the direction of the magnetic field measured by themagnetometer. Based on expression (1), the magnitude of a signal formagnetic flux density observed in each case will be figured out.

When considering a signal resulting from rotational motion of a magneticmoment, attention may be paid only on a time-variable component of themagnetic moment, that is, a magnitude orthogonal to the axis of therotation. In the below description, the magnetic moment m_(S) isdescribed as one pointing to a direction orthogonal to the axis of therotation. Furthermore, the wavelength of an electromagnetic wave at aresonant frequency is sufficiently longer than an attentioned scale, andthus, can be handled with quasi-static approximation. Furthermore, φrepresents the phase of oscillation.

1) A case where the axis of rotation in the magnetic resonance points toa direction pointing to the signal source viewed from the magnetometer

1-A: Magnetic flux density in the direction pointing to the signalsource viewed from the magnetometer

This direction is that of the axis of rotation, and thus, a magneticflux density in this direction does not vary.

1-B: Magnetic flux density in the direction orthogonal to the axis ofrotation

Since the term of the inner product of the vector, n·m_(S), is zero inexpression (1), a signal expressed by

B(t)=[μ₀ ×m _(S)/(4π×d ₁ ³)]×e ^((−iωt+φ))  (6)

can be obtained.

2) A case where the axis of rotation in the magnetic resonance isorthogonal to the direction pointing to the signal source viewed fromthe magnetometer

2-A: Magnetic flux density in the direction pointing to the signalsource viewed from the magnetometer (vector n direction)

Since the vector n(n·m_(S)) is observed for the second term within thesquare bracket in expression (1), a signal expressed by

B(t)=[μ₀×2m _(S)/(4π×d ₁ ³)]×e ^((−iωt+φ))  (7)

is measured.

2-B: Magnetic flux density in the direction parallel to the axis ofrotation

-   -   Since contribution from 3n(n·m_(S)) in the first term in the        square bracket in expression (1) is zero, a signal expressed by

B(t)=[μ₀ ×m _(S)/(4π×d ₁ ³)]×e ^((−iωt++φ))  (8)

can be obtained according to the rotation of the vector m_(S).

It can be understood from the above description that in observation of amagnetic resonant signal, where a magnetic field in the vector ndirection is measured with an arrangement in which the axis of rotationin the magnetic resonance (direction of the pump beam) is orthogonal tothe direction pointing to the signal source (vector n direction) viewedfrom the magnetometer (2-A), a signal with a magnitude twice those ofthe other cases can be observed.

In an optical gradiometer, also, provision of an arrangement in whichthe respective optically pumped magnetometers operate as described aboveaccording to each of a zero-magnetic field magnetometer and a resonantoperation of a magnetometer enables extraction of a large signal,whereby higher sensitivity measurement can be made.

According to the knowledge described above, the present inventionrelates to a magnetometer using optically pumped magnetometers forming aconfiguration in which two magnetic field measurement regions arearranged so as to be linear with respect to a signal source, and adirection of a magnetic moment m_(S) points a direction from the signalsource to the two magnetic field measurement regions (vector ndirection).

Furthermore, in the zero-magnetic field magnetometer, a magnetic forcecan be measured for a magnetic field in a direction orthogonal to both apump beam and a probe beam.

Furthermore, in a resonant operation of the magnetometer, a magneticforce may be measured for not only a magnetic field in the directionorthogonal to both the pump beam and the probe beam but also a magneticfield in the probe direction.

Specific examples of a gradiometer according to the present invention,which has a configuration such as described above, will be indicatedbelow. However, the present invention is not limited to the belowexamples.

Example 1

In FIG. 1, laser beams 1 and 2 for pumping, which arecircularly-polarized beams, are generated from non-illustrated pump beamsources. The laser beams 1 and 2 propagate in parallel to each other ina positive y axis direction. Both are circularly-polarized beams in asame direction. A laser beam 3 for probe is generated from anon-illustrated probe beam source, a cell 8 contains alkali metalencapsulated therein. Polarizing plates 4 and 5 form a crossed nicolarrangement that does not transmit light when no polarization planerotation occurs in the glass cell. A photodetector 7 receives the probebeam. Mirrors 9 and 10 turn the pump beam back. It is desirable that themirrors have a high reflectivity for an incident angle of 45 degrees andare dielectric multilayer mirrors designed to reduce the difference incomplex reflectivity between p wave and s wave. A faraday modulator 6 isdriven by a modulation signal with a frequency ω_(F) from anon-illustrated signal source to modulate a polarization plane of theprobe beam, which is a linearly-polarized beam, with an angle α and thefrequency ω_(F). Where φ is the angle of rotation of the polarizationplane caused by a magnetic field in the cell, an intensity I of thelight passing through a pair of a polarizer and an analyzer in a crossednicol arrangement can be expressed by

$\begin{matrix}\begin{matrix}{I = {I_{0}\mspace{14mu} {\sin^{2}\left\lbrack {\varphi + {\alpha \; {\sin \left( {\omega_{F}t} \right)}}} \right\rbrack}}} \\{\approx {I_{0}\left\lbrack {\varphi^{2} + {2\varphi \; \alpha \; {\sin \left( {\omega_{F}t} \right)}} + {\alpha^{2}{\sin^{2}\left( {\omega_{F}t} \right)}}} \right\rbrack}}\end{matrix} & (9)\end{matrix}$

In other words, a frequency ω_(F) component of the intensity of thelight has an amount proportional to 2I₀αω and the angle of rotation ofthe polarization plane.

An optical path of the laser beam for probe has a route starting from alower left portion of the Figure and extending through a route from thepolarizing plate 4, the faraday modulator 6, the cell 8, the mirror 9,the mirror 10, the cell 8, the polarizing plate 5 and the photodetector7 in this order. Along this route, a region in which the first pump beam1 and the probe beam 3 cross each other is a first measurement position,and a region in which the probe beam turned back by the mirrors 9 and 10crosses the second pump beam 2 is a second measurement position. Thisconfiguration provides a configuration in which the first measurementposition and the second measurement position are arranged along adirection linear with respect to a signal source (first direction).Here, the polarization plane of the probe beam rotates according to thevalue of B_(z1), which is a z component of a magnetic flux density inthe first measurement position, and the value of B_(z2), which a zcomponent of magnetic flux density in the second measurement position.

The cell 8 consists of a material transparent to the probe beam and thepump beams, such as glass. The cell contains K in a gaseous state, whichis hermetically encapsulated. In the cell, a gas functioning as abuffer, such as He, and/or an N₂ gas can also be encapsulated inaddition to the atom group. Since a buffer gas suppress diffusion ofpolarized alkali metal atoms, it is effective to suppress spinrelaxation occurring due to collision with the cell walls, therebyenhancing the polarization ratio. Furthermore, an N₂ gas is a quenchergas that draws energy from K in an excited state to suppress lightemission of K, and is effective for producing large spin polarization inthe alkali metal gas by means of pumping.

A potassium metal is placed in a glass cell and heated to around 180°C., enabling the glass cell to be filled with potassium metal vapor witha number density of around 10¹⁴ cm⁻³. Here, the cell is placed in anon-illustrated oven for heating, and heated to a desired temperature byhot air circulating in the oven.

Furthermore, in the present example, a non-illustrated magnetic shieldand a three-axis Helmholtz coil system are used to decrease geomagnetismand an environmental magnetic field around the cell 8 to no more than 1nT.

In the first measurement position, y-direction spin polarization isproduced by the first pump beam 1, which is a circularly-polarized beamσ⁺. Where a z-direction magnetic field B_(z1) is positive, positive spinpolarization occurs in the x direction. Here, since the probe beam 2,which is a linearly-polarized beam, passing through the firstmeasurement position, travels in the same direction as that of the spinpolarization produced by the pump beam, and thus, the polarization planemakes right-hand rotation according to the magnitude of the spinpolarization.

The optical path of the probe beam is turned back by the mirrors 9 and10 to the cell 8 again. Similarly, in the second measurement position,y-direction spin polarization is produced by the second pump beam 2,which is also a circularly-polarized beam σ⁺, and where a z-directionmagnetic field B_(z2) is positive, positive spin polarization occurs inthe x direction, too. Here, as opposed to the first measurementposition, the probe beam 2 propagates in a direction opposite to thedirection of the spin polarization, and thus, the polarization planemakes left-hand rotation according to the magnitude of the spinpolarization.

Where a rotation angle φ of the polarization plane is represented by amathematical expression, it can be expressed by

φ=cr _(e) fnlP _(x) Re[L(ν)]  (10)

Here, ν is the frequency of the probe beam, n is an atomic density of analkali metal, c is a speed of the light, and r_(e)(=2.82×10⁻¹⁵ m) is aclassical electron radius. Furthermore, f is an oscillator strength ofoptical transition, l is a length of a measurement position, P_(x) is amagnitude of the x-direction spin polarization (up to 1), L(ν) is acomplex Lorenz function of a center wavelength ν₀ and a full width athalf maximum Δν representing a shape of an absorption line. Here, whenthe probe beam is made to propagate in the opposite direction in themeasurement position 2, it should be noted that a negative sign is addedfurther to expression (10).

A specific magnitude of the x-direction spin polarization P_(x) can befigured out from optical Bloch equation (5). Considering a pumpingvector R=(0, R, 0), which is y-direction pumping,

$\begin{matrix}{P_{x} = \frac{R\left( {\gamma_{e}{B_{z}/Q}} \right)}{\Gamma_{eff}^{2} + \left( {\gamma_{e}{B_{z}/Q}} \right)^{2}}} & (11)\end{matrix}$

can be obtained as a stationary solution. Based on expression (11), itcan be understood that if B_(z) is so small that Γ_(eff) >γ_(e)B_(z)/Qcan be provided, a P_(x) which is substantially proportional to B_(z)can be obtained. Combining expressions (10) and (11), it is also clearthat the rotation angle φ of the polarization plane is proportional toB_(x). If this relationship is represented by φ=αB_(z), the rotationangle of the polarization plane of the probe beam that has sequentiallypassed through the first measurement position and the second measurementposition can be expressed by

φ=α_(A1) B _(z1)−α_(A2) B _(z2)=α(B _(z1) −B _(z2))  (12),

and thus, the rotation angle of the polarization plane of the probe beamincident on the photodetector is an amount resulting from magnetic fieldsubtraction as a gradiometer. The latter equal sign in expression (12)is provided where proportionality coefficients α_(A1) and α_(A2) of therotation angles relative to the magnetic fields at the respectivemeasurement positions are substantially equal to each other. Referringto expressions (10) and (11), it can be understood that examples ofparameters to be uniformed to make α_(A1) and α_(A2) to be equal to eachother include, e.g., the alkali metal density n, the length of themeasurement position l the pumping vector R (the intensity of the pumpbeam), the spin polarization ratio (absolute value of the spinpolarization vector P), and a slowdown factor Q, which will bedetermined later.

Under the condition that photon shot noise restricts the sensitivity,the gradiometer configured as described above provides signal/noiseratio improvement twice the gradiometer in which probe beams are made topass through two independent measurement positions, respectively, todetect rotations of the respective polarization planes by means ofphotodetectors (comparison example). The principle will be describedbelow.

Here, P₀ is the number of photons provided to each of the gradiometersaccording to comparative example and the present example per unit time.In comparative example, the photons to be provided are divided in halfand used, and thus, the signal in each photodetector is proportional toP₀/2. Furthermore, shot noise in each photodetector is proporational to(P₀/2)^(1/2). For the signal, subtraction of the signals from each otherresults in obtainment of the strength proportional to P₀/2. Meanwhile,even though “subtraction” is performed, random ones are added up for thenoise, resulting in (P₀/2+P₀/2)^(1/2)=P₀ ^(1/2). Accordingly, the S/Nratio in comparative example is proportional to an amount expressed by

P₀ ^(1/2)/2  (13).

Meanwhile, in the present example, the signal in the photodetector isproportional to P₀, and the shot noise in the photodetector isproportional to P₀ ^(1/2). Therefore, the S/N ratio is proportional to

P₀ ^(1/2)  (₁₄).

Comparing expressions (13) and (14), it can be understood that thepresent example enables provision of a doubled S/N ratio in measurementusing a same number of photons.

A magnetic moment, which is a signal source, is arranged in a negativedirection on a z-axis in the Figure. As already described above,measurement of a z component of a magnetic field in each of the firstmeasurement region and the second measurement region arranged to belinear with respect to the signal source results in measurement ofrelatively large magnetic signals, enabling provision of highsensitivity.

For the turns of the optical path via the mirrors 9 and 10, it isdesirable to employ a mirror configuration that reduces its effects onthe polarization plane of the probe beam.

Fresnel reflection via a mirror exhibits different reflectivities forp-wave and s-wave. Here, a p-wave is a polarized wave of light whoseelectric field vector is present on an incident plane, and an s-wave isa polarized wave of light whose electric field vector is orthogonal toan incident plane. Use of dielectric multilayer mirrors enablessuppression of the difference in reflectivity between p-wave and s-waveto no more than 1%, which is desirable as a method for turning anoptical path; however, this case also requires the reflection phases tobe taken into consideration.

For optical path turning in a gradiometer such as that in the presentexample, two examples of an optical configuration avoiding the effectsof Fresnel reflectivity's dependency on the polarization plane areindicated below.

1) There are known dielectric multilayer mirrors with a configurationexhibiting a high reflectivity for both p-wave and s-wave with a45-degree incidence. In such high reflectivity mirrors, phases ofreflection are not uniform but diffused depending on the wavelengths.Therefore, in order to enable precise measurement of the polarizationplane, an optical system that turns an optical path through a reflectionroute including a plurality of reflective planes, such as illustrated inFIGS. 2A and 2B, is used. In this optical system, on a plane includingan optical path for light to enter the optical system and an opticalpath for light to exit from the optical system, there are tworeflections whose angle of incident on a mirror is 45 degree.Furthermore, on a plane perpendicular to the optical path for light toenter the optical system and the optical path for light to exit from theoptical system, there are two reflections whose angle of incidence onrespective mirrors is 45 degrees. As a result, in the reflection routeof light with an e_(y) polarized wave, the reflections occur for thep-wave, the s-wave, the s-wave and the p-wave in this order, while inthe reflection route of light with an e_(z) polarized wave, thereflections occurs for the s-wave, the p-wave, the p-wave and the s-wavein this order.

FIG. 2A is a perspective view of the mirrors, and FIG. 2B illustratesthree planes of the mirrors using trigonometry. Consequently, a phaseshift amount resulting from the reflections in the entire optical pathturn is the same regardless of the p-wave incidence or the s-waveincidence, enable elimination of the effect of the optical path turn onmeasurement of the polarization plane.

2) As a unit for substituting the reflections via the mirrors 9 and 10,it is possible to turn the optical path by means of total reflectionusing a prism. In total reflection, there is a difference in phase shiftamount due to reflection between p-waves and s-waves, hindering precisemeasurement of a rotation of the polarization plane. Therefore, use of aprism such as illustrated in FIGS. 3A and 3B enables provision of anoptical system with an optical path turn in which in a route of theoptical path turn, there are a sum of four total reflections, i.e., twototal reflections for incidence of a p wave and two total reflectionsfor incidence of a s wave. In other words, in the total reflection routeof light with the e_(y) polarized wave, the reflections occur for the pwave, the s wave, the s wave and the p wave in this order, while in thetotal reflection route for light with the e_(z) polarized wave,reflections occur for the s-wave, the p-wave, the p-wave and the s-wavein this order.

FIG. 3A is a perspective view of the prism, and FIG. 3B illustratesthree planes of the prism using trigonometry.

Although an example has been provided focusing on an operation of azero-magnetic field magnetometer here, a resonant operation can beperformed using the same configuration.

The resonant operation can be performed by adjusting a current flowingin the non-illustrated Helmholtz coil system to apply a bias magneticfield in the pump beam direction, thereby making the spinning of thealkali metal to precess at a frequency ω. The arrangement according tothis example is particularly favorable for measurement of an oscillatingmagnetic field in the B_(z) direction by resonant operation.

Example 2

FIG. 4 illustrates another configuration of a gradiometer usingmagnetometers using a resonant operation. The second example isdifferent from the first example in that no optical turn using mirrorsis provided on an optical path of probe beam.

The second example is characterized in an arrangement in which a firstpump beam 1 and a second pump beam 2, which correspond to twomeasurement regions, respectively, are circularly-polarized beams thatrotate along a same direction but are incident on the cell 8 indirections opposite to each other, which is the difference from that ofthe first example. The circularly-polarized beams may have eitherright-hand rotation or left-hand rotation as long as thecircularly-polarized beams rotate along the same direction. Furthermore,in the present example, there is a system that detects a rotation of apolarization plane by means of a balance photodetector including apolarization separation optical element 11 and photodetectors 12 and 13.

A first measurement region is a region in which a probe beam 3 made tobe a linearly-polarized beam by a polarizer 4 cross the first pump beam1, which is the circularly-polarized beam with right-handed rotation andis arranged inside a cell 8. Here, a DC current is made to flow in anon-illustrated Helmholtz coil pair to apply a magnetostatic field tothe entire cell in an x-direction. A magnetostaic field of around 0.7 μTis applied so that spin polarization of potassium excited in the cellprecesses at a Larmor frequency of 5 kHz. The first pump beam 1 producesspin polarization in the x direction, and this spin polarizationresonates with oscillating magnetic field components of around 5 kHzwhile preccessing at 5 kHz. Here, the magnetometer has sensitivity to,in particular, y-direction and z-direction magnetic fields.Consequently, according to B_(y) and B_(z) magnetic fields oscillatingat the resonant frequency, a z-component of the spin polarizationoscillating at that frequency occurs, and thus, an angle of rotation ofthe polarization plane of the probe beam passing through the firstmeasurement region is one periodically modulated at a resonant frequencyof 5 kHz.

Similarly, in the second measurement region in which the second pumpbeam 2, which is a circularly-polarized beam with right-hand rotation,and the probe beam 3 cross each other in the cell 8, spin polarizationis produced by the pump beam, an x-component of the spin polarization isone having a sign that is the reverse of that of the spin polarizationin the first measurement region. A bias magnetic field, which hasalready been described, is applied also to the second measurementregion, and the spin polarizations have precession motion in a samedirection (without depending on the signs of the respectivepolarizations). Furthermore, as with the resonance in the firstmeasurement region, a z-direction component is generated in the spinpolarization as a result of resonance with an oscillating magneticfield. Under the condition that resonant magnetic fields of a completelysame magnitude and direction are measured in the first measurementregion and the second measurement region (this is an assumed conditionfor description), the z-direction spin polarization has a sign oppositeto that of the first measurement region, reflecting the reverse sign ofthe x-direction spin polarization. Therefore, an angle of rotation ofthe polarization plane of the probe beam passing through the secondmeasurement region is one further periodically modulated at a resonantfrequency of 5 kHz, contribution of the polarization plane rotation inthe second region is one with a sign opposite to that of contribution inthe first region.

Thus, it can be understood that the angle of rotation of thepolarization plane of the probe beam sequentially passed through thefirst measurement position and the second measurement position can beexpressed by

φ=α_(A1) B _(z1)−α_(A1) B _(z2)=α_(A1)(B _(z1) −B _(z2)),

which enables formation of a magnetic field gradiometer.

A direction of a polarizer 4 determining the polarization plane of theprobe beam is adjusted so that when the angle of rotation of thepolarization plane in the cell 8 is 0, an amount of reflected light andan amount of transmitted light in the polarized beam splitter 11 areequal to each other. In other words, an arrangement is made so that apolarizing axis of the polarized beam splitter 11 and a polarizationplane of light passing through the polarizer 4 form an angle of 45degrees. Obtainment of a difference between optical power received bythe photodetector 12 and optical power received by the photodetector 13enables extraction of an electric signal according to the angle ofrotation of the polarization plane.

For a layout for obtaining a magnetic resonant signal, a magneticmoment, which is a signal source rotating by means of magneticresonance, is arranged at a negative position on the z axis in theFigure. As already described, measurement of a z-component of a magneticfield in each of the first and second measurement regions arranged to belinear with respect to the signal source results in measurement ofrelatively large magnetic signals, enabling provision of highsensitivity. In such arrangement, in order to prevent the distancebetween the first measurement region and the signal source from beinglarge, it is effective to bend an optical path of the probe beamentering the polarizer 4 in the Figure, using an optical path changingunit such as a non-illustrated mirror or a prism.

For magnetic field measurement using a resonant operation, not onlyrotation of a magnetic moment, which is a signal source, and rotation ofspin polarization to have frequencies corresponding to each other orfalling within a range of a resonance width, but also the rotationdirections to be correspond to each other, is required. Therefore, it isnecessary that a direction of the bias magnetic field B_(z) applied tothe cell 8 correspond to a direction of a x-component of a magnetostaticfield B₀ in which the signal source is placed for generating magneticresonance in the signal source. Furthermore, a magnitude of the magneticfield should be selected according to a gyromagnetic ratio of a nuclideused for the magnetic resonance.

In order to achieve a state in which signs of spin polarizationgenerated in the first measurement region and in the second measurementregion as a result of optical pumping are different from each other,another configuration can also be employed. In a variation of thepresent example, which is illustrated in FIG. 5, a first pump beam 1 anda second pump beam 2 corresponding to two measurement regions arecircularly-polarized beams propagating in a same direction, butdirections of rotations of the circularly-polarized beams are differentfrom each other, causing spin polarization to be generated in the firstmeasurement region and the second measurement region in directionsopposite to each other.

Operation of the magnetometer using a resonant operation is similar tothat of the present example described, and thus, description thereofwill be omitted.

Example 3

Another example in which rotations of a polarization plane of a probebeam by a magnetic field, which are measured in a first measurementregion and a second measurement region, have directions opposite to eachother will be described with reference to FIG. 6. In FIG. 6, a half-waveplate 14 is inserted between the first measurement region and the secondmeasurement region along an optical path of the probe beam. A crystalaxis direction of the half-wave plate 14 is made to correspond to adirection of a polarization plane of light passing through a polarizer4. Where φ is a rotation of the polarization plane in the firstmeasurement region, an angle of rotation of the polarization plane ofthe probe beam passing through the half-wave plate 14 is −φ. This isbecause change of a polarization state when the probe beam passingthrough the half-wave plate arranged as described above can be expressedby the following matrix where a set of electric field vectors (e_(x),e_(y))^(T) is a base thereof.

${\exp \left( {\; \phi} \right)}\begin{pmatrix}1 & 0 \\0 & {- 1}\end{pmatrix}$

Although FIG. 6 illustrates that a cell 8 a and a cell 8 b areindependent cells, it is necessary to make a first measurement positionand a second measurement position correspond to each other in terms of,e.g., alkali metal density n, measurement position length l pumpingvector R, spin polarization ratio and slowdown factor Q which will bedetermined later as in example 1. Thus, a configuration in which thesecells are interconnected via a non-illustrated path may be employed. Theinterconnection of the cells as described above is effective to providea common alkali metal density in the two measurement regions to make thetwo measurement regions in the gradiometer have equal parameters.

Although the polarization plane of the probe beam subsequently passingthrough the second measurement region further rotates, contribution ofthe polarization plane rotation in the second region has a sign oppositeto that of contribution in the first region.

Furthermore, in the present example, as in the second example, aresonant operation of a magnetometer is performed on a y-direction biasmagnetic field, providing sensitivity to B_(z), enabling a gradiometerthat measures a large signal from a magnetic moment. While the presentinvention has been described with reference to exemplary embodiments, itis to be understood that the invention is not limited to the disclosedexemplary embodiments. The scope of the following claims is to beaccorded the broadest interpretation so as to encompass all suchmodifications and equivalent structures and functions.

While the present invention has been described with reference toexemplary embodiments, it is to be understood that the invention is notlimited to the disclosed exemplary embodiments. The scope of thefollowing claims is to be accorded the broadest interpretation so as toencompass all such modifications and equivalent structures andfunctions.

This application claims the benefit of Japanese Patent Application No.2010-181414, filed Aug. 13, 2010, which is hereby incorporated byreference herein in its entirety.

1. A gradiometer using an optically pumped magnetometer, the gradiometerusing the optically pumped magnetometer comprising: one or more cellseach containing a group of atoms in a gaseous state, including an alkalimetal, encapsulated therein; a pump beam source that applies a firstpump beam and a second pump beam to each of the one or more cells tospin-polarize the group of atoms, the first pump beam and the secondpump beam being parallel to each other; a probe beam source that appliesa probe beam to the one or more cells to which the pump beams have beenapplied; a detector for detecting a rotation of a polarization plane ofthe probe beam that has passed through the one or more cells in a statein which the group of atoms is spin-polarized, wherein the first pumpbeam and the probe beam cross each other at a first measurementposition, the second pump beam and the probe beam crosses each other ata second measurement position, the first measurement position and thesecond measurement position are arranged along a first direction that islinear with respect to a signal source, and the probe beam sequentiallypasses through the first measurement region and the second measurementregion; wherein an alkali metal density, a measurement position length,a pump beam intensity and a spin polarization ratio for the firstmeasurement position are the same as those of the second measurementposition; and wherein each of a direction of a magnetic field measuredat the first measurement position and a direction of a magnetic fieldmeasured at the second measurement position is the same as the firstdirection, a sign of spin polarization caused by optical pumping isdifferent between the first measurement region and the secondmeasurement region; and an angle of rotation of the polarization planeof the probe beam that has sequentially passed through each of the firstmeasurement position and the second measurement position is obtained,thereby obtaining a difference in magnetic flux density between thefirst measurement position and the second measurement position.
 2. Thegradiometer using the optically pumped magnetometer according to claim1, wherein a direction of the rotation of the polarization plane of theprobe beam at the first measurement position is opposite to a directionof the rotation of the polarization plane of the probe beam at thesecond measurement position.
 3. The gradiometer using the opticallypumped magnetometer according to claim 1, comprising a half-wave platebetween the first measurement region and the second measurement region.4. The gradiometer using the optically pumped magnetometer according toclaim 2, wherein the first measurement position and the secondmeasurement position are provided in a same one of the one or morecells; and an optical path changing unit for reversing a direction oftravel of the probe beam that has passed through the first measurementposition to make the probe beam pass through the second measurementposition is provided.
 5. The gradiometer using the optically pumpedmagnetometer according to claim 2, wherein the first measurementposition and the second measurement position are provided in a same oneof the one or more cells; the first pump beam applied to the firstmeasurement position and the second pump beam applied to the secondmeasurement position both have one of right-hand circular polarizationand left-hand circular polarization; and the first pump beam and thesecond pump beam propagate in the one or more cells in directionsopposite to each other.
 6. The gradiometer using the optically pumpedmagnetometer according to claim 2, wherein the first measurementposition and the second measurement position are provided in a same oneof the one or more cells; the first pump beam applied to the firstmeasurement position and the second pump beam applied to the secondmeasurement position are circularly-polarized beams whose directions ofrotation are different from each other; and the first pump beam and thesecond pump beam both propagate in the cell in a same direction.
 7. Thegradiometer using the optically pumped magnetometer according to claim4, wherein the optical path changing unit includes an optical elementincluding a plurality of reflective planes; wherein an optical path ofthe optical element includes two reflections, in which an angle ofincident on a mirror is 45 degrees, on a plane including an optical pathin which light enters the optical element and an optical path in whichlight exits from the optical element; and the optical path of theoptical element includes two reflections, in which an angle of incidenton a mirror is 45 degrees, on a plane perpendicular to the optical pathin which light enters the optical element and the optical path in whichlight exits from the optical element.